Rules for Reduced Row Echelon Form? (video left me confused)

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OK, so I bring this up because I find working with matrices could potentially be very useful.

Watched a couple videos on how to put things in Reduced Row Echelon Form. The first video (https://www.khanacademy.org/math/li...ination/v/matrices-reduced-row-echelon-form-1) I watched ended up being over my head at the endish part of it.
The second video (https://www.khanacademy.org/math/pr...ination/v/matrices-reduced-row-echelon-form-2) I watched made a lot more sense.

But I still have a couple questions regarding what you can actually do to zero out or otherwise manipulate a matrix..

I know you can multiply a row by any real number (and divide as well I am assuming).
I also know you can add or subtract a row by another row.
I also know you can multiply (or divide) a row and then add or subtract that row from another row.

What I don't know, is if you can simply add or subtract a row by any real number.
I am also wondering if you can multiply by an exponent or square root a row. This implies that there are certain matrices with either exponents or square numbers in them and I am wondering how that works. Like can you put trinomials in matrix form and how would you solve them?
Basically I just want to know all the things you can do with Matircies to get to Reduced Row Echelon Form, so if there is a resource that talks about the rules about what you can do with matrices, I would like to see it.
 
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… (https://www.khanacademy.org/math/li...ination/v/matrices-reduced-row-echelon-form-1) I watched ended up being over my head at the endish part of it.
If you provide a time stamp, and then explain the parts you're not sure about, we can help explain specific points.

The second video (https://www.khanacademy.org/math/pr...ination/v/matrices-reduced-row-echelon-form-2) I watched made a lot more sense.

But I still have a couple questions regarding what you can actually do to zero out or otherwise manipulate a matrix..

I know you can multiply a row by any real number (and divide as well I am assuming).
I also know you can add or subtract a row by another row.
I also know you can multiply (or divide) a row and then add or subtract that row from another row.

What I don't know, is if you can simply add or subtract a row by any real number.
Google keywords gaussian elimination rules. :cool:

I am also wondering if you can multiply by an exponent or square root a row.
You may not take roots of rows.

Can you give an example of what you're thinking, regarding multiplication "by an exponent"? Thanks.
 
If you provide a time stamp, and then explain the parts you're not sure about, we can help explain specific points.

At 7:33 he starts talking about making the number above the 1 a 0. IDK why he does that. (this was answered when I looked up Gaussian elimination rules, thanks!)

Google keywords gaussian elimination rules. :cool:

You may not take roots of rows.

Can you give an example of what you're thinking, regarding multiplication "by an exponent"? Thanks.

OK, so I already think I understand this after thinking about it a bit. But what I was thinking is this:

What if you are trying to solve for something like this:

2X^2 + x + 6y - 4 = 12
4X^2 -2x + 1y -17= 28
X^2 +3x + 4y+10= 3

How would you solve this with the exponent on the X's?
 
In the first video when he gets to 12:43 I have no idea what he is talking about.
 
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